Comments on Partial Sums of Harmonic Series
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Partial Sums of Harmonic Series
Given an positive integer $n$, return the least positive integer $k$ such that the $k$th partial sum of the harmonic series is greater than or equal to $n$. For example, if $n = 2$, then $k = 4$, because $1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} = \frac{25}{12} > 2$.
More Input/Output Examples
Input -> Output
1 -> 1
3 -> 11
4 -> 31
This is code-golf, so shortest code wins.
Japt, 11 10 bytes >0©Òß …
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[Python 3], 35 bytes …
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AppleScript, 178 bytes ``` …
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[Raku], 27 bytes {+ …
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[Scala], 55 bytes ( …
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Stax, 9 bytes Ç≈f♠É↔X+ö …
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[JavaScript (Node.js)], 47 byt …
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[Jelly], 8 bytes İ€S<¬ʋ …
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[J], 23 bytes >:@]^:(>1 …
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JavaScript, 29 bytes …
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Goruby, 38 bytes ``` ->n{dw{ …
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Raku, 27 bytes
{+([\+](1 X/1..*)...*>=$_)}
{ } # Anonymous code block
[\+]( ) # Get the partial sum of
1 X/ # 1 over each of
1..* # All positive integers
...*>=$_ # Take from the list until it is bigger than the input
+( ) # And return the length of the list
This will start to suffer precision issues, but you can add .FatRat to work correctly (but much slower)
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